Geometrical OpticsHard
Question
In an interference arrangement similar to Young′d double-slit experiment, the slits S1 and S2 are illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to have phase difference. The slits are separated by a distance d = 1500. m. The intensity I(θ) is measured as a function of θ, where θ is defined as shown. If Io is the maximum intensity, then I(θ) for 0 ≤ θ ≤ 90o is given by
Options
A.I(θ) = Io / 2 for θ = 30o
B.I(θ) = Io / 4 for θ = 90o
C.I(θ) = Io for θ = 0o
D.I(θ) is constant for all values of θ
Solution
The intensity of light is I(θ) = Iocos2 
where δ =
d sin θ
(a) For θ = 30o
= 300m and d = 150m
∴
∴ I(θ) = I0 cos2
[option (a)]
(b) For θ = 90o
(150) (1) = π
∴
and I(θ) = 0
(c) For θ = 0o, δ = 0,
∴ I(θ) = I0 [option (c)]
where δ =
d sin θ (a) For θ = 30o
= 300m and d = 150m ∴
∴ I(θ) = I0 cos2
[option (a)](b) For θ = 90o
(150) (1) = π ∴
and I(θ) = 0 (c) For θ = 0o, δ = 0,
∴ I(θ) = I0 [option (c)]
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